Vibrator isolator system

ABSTRACT

A vibration isolator system for attaching a payload to a supporting base is provided, the payload having a center of mass and the system consisting of at least three vibration isolating pods. Each pod has two associated, non-parallel, elastic struts. A first end of each strut is attached to the supporting base and a second end of each strut is attached to the payload at a respective mounting point, and the a projected elastic center of the system is substantially co-located with said center of mass. The vibration isolator system is operable to substantially prevent translational vibration of the supporting base from inducing angular rotation of the payload.

CROSS REFERENCE TO RELATED APPLICATION

This application which claims benefit under 35 U.S.C. §§120 and 119(e),is a continuation of U.S. application Ser. No. 13/116,336, filed May 26,2011, which is a continuation of U.S. application Ser. No. 12/400,557,filed Mar. 9, 2009, now U.S. Pat. No. 7,950,633, which claims thebenefit of U.S. Provisional Application No. 61/086,880, filed Aug. 7,2008, the content of which is hereby incorporated into the presentapplication in its entirety.

FIELD OF THE INVENTION

The present invention relates to vibration isolating techniques,particularly techniques for preventing translational vibration of asupporting structure from inducing angular rotation of a payload whileminimizing geometric constraints on structures connecting the payload tothe supporting structure.

BACKGROUND OF THE INVENTION

Vibration isolation is often used to stabilize a payload's angularorientation in the face of translational vibration. The translationalvibration may be self induced by the payload (for example by selfinduced vibration from a motor of a gimbal assembly, or transmitted froma support structure upon which the payload is supported. Rotationalmotion of a payload may be reduced (or nearly eliminated) if the payloadis supported by a suspension system that does not couple linear basemotion vibration into angular motion. Such a suspension system may bereferred to as a vibration isolator system.

Conventionally, such coupling may be prevented by providing elasticmounts (or struts) having attachment points to the payload in a commonplane containing the payload's center of mass (“cm”). This places the“elastic center” of the isolators at the cm of the payload. The meaningof the term “elastic center”, as used herein, may be better understoodby considering a hypothetical suspension system including a plurality ofelastic struts supporting an object, for example, a payload. The elasticcenter of the suspension system is the point at which, if the center ofmass of the body is located at the point, the application of a forcethrough the point would result in a pure translational movement, and theapplication of a moment about the point would result in pure rotation ofthe body about that point.

A problem exists for many system configurations where it is impossibleto provide elastic struts having attachment points to the payload in acommon plane containing the payload's cm. In optical systems, forexample, the area of the cm plane may need to remain clear for theoptical field of view for the optical system. For such systems, theelastic struts must be coupled to an attachment surface of the payloadassembly or system that is substantially distant from the payload's cm.

Attachment points at which the elastic struts connect to the payload maycollectively define a mount plane. As the term is used herein, a“projected elastic center” of elastic struts in a suspension system maybe understood by recognizing that each elastic strut has a respectiveline of action (defined by its longitudinal axis) at an angle oforientation with respect to the mount plane. If the lines of action areeach oriented at 90 degrees to the mount plane, so that the lines areparallel and do not intersect, the elastic center of the suspensionsystem will be in the mount plane (i.e., the elastic center is notprojected). Contrariwise, if the lines of action are not oriented at 90degrees to the mount plane a projected elastic center will generallyexist at some distance from the mount plane.

A special case where the projected elastic center coincides with acenter of mass of the supported body, occurs when the line of action ofeach elastic mount (or “strut”) passes through the center of mass of thesupported body. As illustrated in FIG. 1, for example, a payload 110 issupported from a base structure 102 by elastic struts 103, each strut103 having a line of action passing through the center of mass 120 ofpayload 110.

As disclosed in Denice, Jr., et al., U.S. Pat. No. 6,871,561(hereinafter, “Denice”), when lines of action of elastic mounts (orisolators) intersect at the center of mass of a supported body,cross-coupling of translational vibration into rotational motion can besubstantially eliminated.

Gran, et al., U.S. Pat. No. 6,022,005 (hereinafter, “Gran”) disclosesanother arrangement for preventing the coupling of translationalvibration unwanted rotational movements. According to Gran, three pairsof semi-active isolators are provided. The isolators in each pair arepositioned in a parallel relationship with each other, lying in the sameplane such that a centerline parallel to and midway between the twoisolators of each pair passes through the center of mass of the payload.

The geometric relationships prescribed by the schemes disclosed in Granand Denice are difficult or impossible to achieve in many real worldsituations. Referring now to FIG. 2, for example, where a payloadattachment structure 201 is attached to a base attachment structure 202by several elastic struts 203, available mounting places on therespective attachment structures do not permit the struts 203 to bearranged so that their line of action is directed toward center of mass220 of the payload (not shown).

SUMMARY OF THE INVENTION

The present inventors have recognized that vibration of a support may beprevented from inducing angular rotation of a payload by satisfyinggeometric constraints substantially less restrictive than thosedisclosed in the prior art. For example, in accordance with variousembodiments of the present invention, a projected elastic center may becaused to coincide with a supported object's center of mass even thoughthe lines of action of isolators do not intersect at the supportedobject's center of mass. Neither is it required that parallel struts bedisposed in pairs.

In accordance with systems and apparatuses consistent with the presentinvention, a vibration isolator system for attaching a payload to asupporting base is provided, the payload having a center of mass and thesystem consisting of at least three vibration isolating pods. Each podhas two associated, non-parallel, elastic struts. A first end of eachstrut is attached to the supporting base and a second end of each strutis attached to the payload at a respective mounting point, and the aprojected elastic center of the system is substantially co-located withsaid center of mass. The vibration isolator system is operable tosubstantially prevent translational vibration of the supporting basefrom inducing angular rotation of the payload.

In an embodiment, each respective mounting point is located in a commonmounting plane and the common mounting plane is substantially distantfrom the center of mass.

In a further embodiment, the center of mass is contained in a principalplane and each elastic strut has a respective longitudinal axis having arespective point of intersection with the principal plane where eachrespective point of intersection is equidistant from the center of mass.In some embodiments, each respective mounting point may be located in acommon mounting plane parallel to the principal plane.

In yet a further embodiment, each vibration isolating pod consists oftwo associated co-planar, elastic struts, where each elastic strut has arespective longitudinal axis, and a respective virtual intersectionpoint is associated with each pod, the respective virtual intersectionpoint being a point of intersection between the respective longitudinalaxes of the associated elastic struts within each pod; and the virtualintersection points are co-planar and equidistant from the center ofmass.

Other systems, methods, features, and advantages of the presentinvention will be or will become apparent to one with skill in the artupon examination of the following figures and detailed description. Itis intended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe invention, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate an implementation of the presentinvention and, together with the description, serve to explain theadvantages and principles of the invention. In the drawings:

FIG. 1 shows a payload support system according to the prior art.

FIG. 2 shows a payload support system according to the prior art.

FIG. 3 a depicts a perspective view of an illustrative embodiment of avibration isolation system consistent with the present invention;

FIG. 3 b depicts a plan view of an illustrative embodiment of avibration isolation system consistent with the present invention;

FIG. 3 c depicts an elevation view of an illustrative embodiment of avibration isolation system consistent with the present invention;

FIG. 4 a depicts a plan view of another illustrative embodiment of avibration isolation system consistent with the present invention;

FIG. 4 b depicts an elevation view of another illustrative embodiment ofa vibration isolation system consistent with the present invention; and

FIG. 4 c depicts a perspective view of another illustrative embodimentof a vibration isolation system consistent with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to an implementation in accordancewith methods, systems, and products consistent with the presentinvention as illustrated in the accompanying drawings.

In an embodiment, a supported structure, for example a payload, isattached to a supporting base, for example a vehicle chassis, or othersupporting structure, by at least three vibration isolating pods. Eachpod may consist of two associated, non-parallel, elastic struts.Advantageously, the pods are arranged in such a manner that a projectedelastic center is substantially co-located with said center of mass.

As the term is used herein, an elastic strut (or “strut”) may be anytype of elastic member having a line of action along a correspondinglongitudinal axis. For example, a strut may consist of a simple springelement, or a spring element with a damper element, working together asa shock absorber. In order to provide for substantially linear motionalong the longitudinal axis, linear guides or bushings may be included.Attachment points in the form of spherical bearings may be provided sothat each strut carries predominantly axial loads along its longitudinalaxis. Such bearings may minimize lateral loads perpendicular to thelongitudinal axis or moment loads at the attachment points. Each strutmay be passive, active, or semi-active.

Referring now to FIG. 3, an embodiment will be described and analyzedwherein a hexapod 300 apparatus, connects a payload attachment structure301 to a base structure 302. The following analysis of a stiffnessmatrix for hexapod 300 will illustrate that off-diagonal terms of thestiffness matrix vanish if certain geometrical conditions are satisfied.In such case, a passive isolation system may be provided in which thespring stiffness characteristics in all six degrees of freedom areindependent and decoupled from one another.

Hexapod 300 may be modeled as six idealized elastic struts 303, eachhaving a first end attached to supporting base 302 and a second endattached to payload attachment structure 301 (FIG. 3 c). Attachmentpoints 307 and 309 represent interface between the elastic struts and,respectively the payload attachment structure 301 and supporting base302 (FIG. 3 a). Each strut may be characterized by its length and itsaxial stiffness, k (lb/in). Advantageously, ball joints at the ends ofeach strut 303 may provide that the struts act only in tension andcompression. Moreover, each strut 303 may include some mechanism fordamping.

As illustrated in FIG. 3 b, hexapod 300 may consist of three bipods 305,each bipod consisting of two associated, non-parallel, struts 303. Thethree bipods 305 may be distributed symmetrically around an X-axis thatis perpendicular to a plane defined, for example, by a plane containingrespective mounting points 307. For convenience, the X-axis will bedefined as vertical in the following discussion, but such definition isnot limiting on the present invention.

In an embodiment, each of three bipods 305 consists of a pair of struts303. Each bipod 305 may be configured such that both of struts 303 in agiven bipod 305 reside in a common vertical plane parallel to axis X. Asillustrated in FIG. 3 b, each of the three bipods may be disposedequidistant from the X-axis at a radial distance R.

Referring now to FIG. 3 c, one end of each of the struts 303 may beanchored to supporting base 302. Attachment points 309 may connect eachstrut 303 to supporting base 302 in a base plane, defined as plane A,orthogonal to the X-axis. A second end of each strut 303 may be attachedto payload attachment structure 301 at a respective mounting point 307.The respective mounting points 307 may define a second plane, parallelto plane A, identified as plane B.

In an embodiment, struts 303 making up a respective bipod 305 areconfigured such that their longitudinal axes intersect at a virtualintersection point (“vertex”) 311 located in the bipod plane.Advantageously, for each bipod 305, a respective vertex 311 lies in acommon plane, plane C, parallel to plane A and plane B. A characteristicangle, θ, is defined as the angle a strut 305 makes with a verticalline. Advantageously, angle θ may be identical for each strut in eachbipod.

As demonstrated in the following analysis, the geometry of FIG. 3 willresult in a projected elastic center being located on the X-axis atplane C, provided only that each bipod 305 is equidistant from axis X(e.g., at radius R) and has a common characteristic angle, θ. Forpurposes of the following analysis, an arbitrary YZ plane of an XYZcoordinate system of a payload will be defined to coincide with plane C.

To determine and describe the stiffness characteristics of the hexapodillustrated in FIG. 3, the stiffness method (also called thedisplacement method) commonly used in finite element analysis, may beutilized. This method is documented, for example, in Rubenstein, MosheF., Matrix Computer Analysis of Structures, N.J.: Prentice-Hall Inc.,1966.

Expressed in matrix form, the stiffness method models the relationshipbetween forces and displacements according to equation (1):

{F}=[K]{u}  (1)

where,

-   -   {F} is a column matrix of system forces, acting on the hexapod;    -   {u} is a column matrix of system displacements; and    -   [K] is the system stiffness matrix.

For the present case, the elements of displacement matrix {u} may bedefined as:

u₁=x-axis translation (inches);

u₂=y-axis translation (inches);

u₃=z-axis translation (inches);

u₄=x-axis rotation (radians);

u₅=y-axis rotation (radians); and

u₆=z-axis rotation (radians).

The elements of force matrix {F} may be defined as:

F₁=x-axis force (lbs);

F₂=y-axis force (lbs);

F₃=z-axis force (lbs);

F₄=x-axis moment (in-lb);

F₅=y-axis moment (in-lb); and

F₆=z-axis moment (in-lb).

System stiffness matrix [K] may be generated from the stiffnesscharacteristics of individual strut elements as illustrated by equation(2):

{P}=[κ]{δ}  (2)

where,

-   -   {P} is a 6×1 column matrix of element forces    -   {δ} is a corresponding 6×1 column matrix of element        displacements, and    -   [κ] is a 6×6 element stiffness matrix.

For hexapod 300, each of the six struts may be characterized by a onedimensional relationship as illustrated by equation (3):

P _(i)=κ_(i)δ_(i) for i=1-6  (3)

Where P_(i) and δ_(i) are the displacement and element force,respectively of strut ‘i’.

Positive P_(i) may defined as tension and positive δ_(i) may be definedas extension. For hexapod 300, when all six element stiffnesses areequal to k, κ_(ij)=k, for i=j; while κ_(ij)=0 for i≠j. The relationshipbetween system displacements and element displacements is expressed inequation (4) in terms of compatibility matrix, [β], where,

{δ}=[β]{u}  (4)

For hexapod 300, compatibility matrix [β], according to smalldisplacement theory, is:

cos θ 0 −sin θ   R sin θ 0 R cos θ cos θ 0   sin θ −R sin θ 0 R cos θcos θ   ½√3 sin θ   ½ sin θ   R sin θ −½√3 R cos θ −½ R cos θ cos θ −½√3sin θ −½ sin θ −R sin θ −½√3 R cos θ −½ R cos θ cos θ −½√3 sin θ   ½ sinθ   R sin θ   ½√3 R cos θ −½ R cos θ cos θ   ½√3 sin θ −½ sin θ −R sin θ  ½√3 R cos θ −½ R cos θ

The first column of compatibility matrix [β] represents the six elementdisplacements (δ₁ to δ₆) for a unit system displacement u₁ in theX-direction. Unit displacement u₁ in the X-direction produces adisplacement of each strut equal to u₁ cos θ. Because of symmetry, allsix struts experience the same displacement. The second column ofcompatibility matrix [β] contains the strut displacements due to a unitsystem displacement, u₂ in Y-direction. Displacement u₂ causes no motionin struts 1 and 2 because they lie in a plane that is perpendicular tothe motion. Struts 3 thru 6 have alternating extension and compressionmotion due to their orientation with respect to the Y-axis. Theremaining elements in compatibility matrix [β] are provided based on thesame small displacement principles.

Further in accordance with the stiffness method, system stiffness matrix[K] may be generated from compatibility matrix [β] and element stiffnessmatrix [κ] according to equation (5):

[K]=[β] ^(T)[κ][β]  (5)

As noted above, the values of element stiffness matrix [κ] are κ_(ij)=kfor i=j; and κ_(ij)=0 for i≠j. As a result, [κ]=k [I], where k is ascalar value and [I] is a unit identity matrix. As a result, equation(5) may be simplified to equation (6):

[K]=k[β] ^(T)[β]  (6)

Stiffness matrix [K], according to equation (6) is shown below:

6 k 0 0 0 0 0 cos² θ 0 3 k 0 0 0 0 sin² θ 0 0 3 k 0 0 0 sin² θ 0 0 0 6 kR² 0 0 sin² θ 0 0 0 0 3 k R² 0 cos² θ 0 0 0 0 0 3 k R² cos² θ

Since stiffness matrix [K] has no off-diagonal terms, all 6 degrees offreedom are decoupled from each other and may be treated independently.Because this is the definition of the “elastic center” of a system, theforegoing shows that the elastic center is located at the origin of theselected coordinate system, i.e., at the intersection of the X-axis andPlane C, where plane C is defined by the three bipod vertices 311 andthe X-axis is the axis of symmetry of hexapod 300. It will be evidentthat by adjusting angle θ, plane C can be moved to any desired distancefrom plane B.

Moreover, the foregoing teachings permit a hexapod support system to bedesigned that provides a projected elastic center coinciding with asupported object's center of mass. That is, the projected elastic centerwill coincide with a supported object's cm if one defines radius R withrespect to a vertical axis passing through the supported object's cm,and judiciously selects angle θ, so that plane C is located at adistance from plane B corresponding to the vertical location of thesupported object's cm.

Thus, increased flexibility to the structural design is provided,because, for example, the lines of action of the strut elements are notrequired to intersect at the supported object's center of mass and thestrut elements are not required to be parallel.

The foregoing stiffness matrix [K] may be expressed in equation formrelative to the XYZ coordinate system as shown in equation set (7)

K _(X)=6k cos² θ

K _(Y) =K _(Z)=3k sin² θ

K _(φx)=6kR ² sin² θ=2R ² K _(Y)

K _(φy) =K _(φz)=3kR ² cos² θ=½R ² K _(X)  (7)

From equation set (7), it is evident that the three translationalstiffnesses, K_(X), K_(Y), and K_(Z) are a function of the angle θ andthe strut axial stiffness ‘k’, but are independent of the location ofplanes A and B or the radius R. The angular stiffnesses, K_(φx), K_(φy),and K_(φz) are a function of parameters k, θ, and R, but are likewiseindependent of the location of planes A and B.

The preceding analysis was for a hexapod configuration. However, thesame results may be achieved using an octapod (8-strut) or highernumbered configuration. The generalized results for ‘n’ struts, eachwith stiffness ‘k’, where ‘n’ is an even number of six or more areprovided as equation set (8):

K _(X) =nk cos² θ

K _(Y) =K _(Z)=½nk sin² θ

K _(φx)=2R ² K _(Y)

K _(φy) =K _(φz)=½R ² K _(X)  (8)

Referring now to FIG. 4, the foregoing analysis may be furthergeneralized to include configurations in which the bipod pairs havenon-coplanar struts. FIG. 4 a provides a view of a hexapod 400 apparatusobserved along the X-axis, which, for purposes of the followinganalysis, remains defined as vertically oriented. The six struts 403 arearranged symmetrically around the X-axis, but no two of them arerequired to occupy a common vertical plane—they may each have their ownvertical plane. The vertical plane of each strut 403 may be located adistance R from the X-axis.

Within the vertical plane of a given strut 403, certain geometricalrelationships may be observed. For example, strut 403(1) may becharacterized by the triangle ‘bed’, illustrated in FIGS. 4 b and 4 c.The point ‘b’ may be defined as the virtual intersection of the line ofaction of strut 403(1) with the plane that contains the X-axis and thatis orthogonal to the vertical plane containing strut 403(1). FIG. 4 billustrates hexapod 400 viewed along a line normal to the planecontaining strut 403(1). Strut angle θ is shown to be the angle fromvertical of strut 403(1). As with each of the other five strut planes,the plane containing strut 403(1) is perpendicular to plane A and offsetfrom the X-axis by a distance R. FIG. 4 c illustrates hexapod 400 inisometric view, and shows that virtual intersection point ‘b’ may definea location of plane C, parallel to planes A and B, along the X-axis.

As illustrated in FIG. 4, all six struts may be disposed symmetricallyaround the X axis and have a common angle θ. In such configuration, theline of action of each strut will intersect plane C at a pointequidistant from the X-axis. The present inventors have found that theelastic center of hexapod 400 is located in the center of Plane C. As inthe preceding analysis performed for hexapod 300, the stiffness matrixwill be decoupled and equation set (7) will apply.

It will be evident that, by judicious selection of angle θ, plane C canbe formed at any desired distance from plane B. More specifically, theforegoing teachings permit a hexapod support system to be designed thatprovides a projected elastic center coinciding with a supported object'scenter of mass even though the lines of action of isolators do notintersect at the supported object's center of mass and even though notwo struts are co-planar. Moreover, any distance R may be selected,thereby providing additional flexibility to a system designer.

The preceding analysis was for a hexapod configuration. However, thesame results may be achieved with a larger number of struts. Thegeneralized results for n struts, each with stiffness k, where n is aneven number of 6 or more are provided as equation set (8).

From the foregoing teachings, it may be inferred that the criticalgeometrical relationships are the position of the vertical plane of thestrut axes and the angular orientation of the strut axes. A projectedelastic center coinciding with a supported object's center of mass maybe provided without regard to strut length and without regard to thelocations of Planes A and B. Thus, for example, the strut lengths do notneed to be equal to each other and the attachment points need not belocated on common planes A and B.

Thus, techniques for preventing translational vibration of a supportfrom inducing angular rotation of a payload while minimizing geometricconstraints on structures connecting the payload to the support havebeen disclosed. The foregoing description of an implementation of theinvention has been presented for purposes of illustration anddescription. It is not exhaustive and does not limit the invention tothe precise form disclosed. Modifications and variations are possible inlight of the above teachings or may be acquired from practicing theinvention.

Accordingly, while various embodiments of the present invention havebeen described, it will be apparent to those of skill in the art thatmany more embodiments and implementations are possible that are withinthe scope of this invention. Accordingly, the present invention is notto be restricted except in light of the attached claims and theirequivalents.

1. An apparatus for attaching a supported structure to a supportingbase, said supported structure having a center of mass, said apparatuscomprising: at least three vibration isolating pods, each said podcomprising two associated, non-parallel, elastic struts, a first end ofeach said strut attached to the supporting base and a second end of eachsaid strut attached to the supported structure at a respective mountingpoint, wherein the apparatus has a projected elastic centersubstantially co-located with said center of mass.
 2. The apparatus ofclaim 1, wherein said apparatus is operable to substantially preventtranslational vibration of the supporting base from inducing angularrotation of the supported structure.
 3. The apparatus of claim 1,wherein each said respective mounting point is located in a commonmounting plane and said common mounting plane is substantially distantfrom said center of mass.
 4. The apparatus of claim 1, wherein: saidcenter of mass is contained in a principal plane and each elastic struthas a respective longitudinal axis having a respective point ofintersection with the principal plane; and each said respective point ofintersection is equidistant from said center of mass.
 5. The apparatusof claim 4, wherein each said respective mounting point is located in acommon mounting plane parallel to the principal plane.
 6. The apparatusof claim 1, wherein each vibration isolating pod comprises twoassociated co-planar, elastic struts, each elastic strut has arespective longitudinal axis, a respective virtual intersection point isassociated with each pod, said respective virtual intersection pointbeing a point of intersection between the respective longitudinal axesof the associated elastic struts within each pod; and said virtualintersection points are co-planar and equidistant from the center ofmass.
 7. The apparatus of claim 6, wherein said virtual intersectionpoints are not co-located.
 8. The apparatus of claim 1, wherein theelastic struts are passive.
 9. The apparatus of claim 1, wherein thesupported object is a payload.
 10. The apparatus of claim 9, wherein thepayload is a gimbal assembly.
 11. A system, comprising a payload havinga center of mass; and a supporting base, said payload attached to saidsupporting base by apparatus comprising: at least three vibrationisolating pods, each said pod comprising two associated, non-parallel,elastic struts, a first end of each said strut attached to the supportand a second end of each said strut attached to the payload at arespective mounting point, wherein the apparatus has a projected elasticcenter substantially co-located with said center of mass.
 12. The systemof claim 11, wherein said apparatus is operable to substantially preventtranslational vibration of the supporting base from inducing angularrotation of the supported structure.
 13. The system of claim 11, whereineach said respective mounting point is located in a common mountingplane and said common mounting plane is substantially distant from saidcenter of mass.
 14. The system of claim 11, wherein: said center of massis contained in a principal plane and each elastic strut has arespective longitudinal axis having a respective point of intersectionwith the principal plane; and each said respective point of intersectionis equidistant from said center of mass.
 15. The system of claim 14,wherein: each said respective mounting point is located in a commonmounting plane parallel to the principal plane.
 16. The system of claim11, wherein: each vibration isolating pod comprises two associatedco-planar, elastic struts, each elastic strut has a respectivelongitudinal axis, a respective virtual intersection point is associatedwith each pod, said respective virtual intersection point being a pointof intersection between the respective longitudinal axes of eachassociated elastic strut within each pod; and said virtual intersectionpoints are co-planar and equidistant from the center of mass.
 17. Thesystem of claim 16, wherein said virtual intersection points are notco-located
 18. The system of claim 11, wherein the elastic struts arepassive.
 19. The system of claim 11, wherein the payload is a gimbalassembly.